Problem: Simplify the following expression: $t = \dfrac{-100r}{-70r - 110}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-100r = - (2\cdot2\cdot5\cdot5 \cdot r)$ The denominator can be factored: $-70r - 110 = - (2\cdot5\cdot7 \cdot r) - (2\cdot5\cdot11)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $t = \dfrac{(10)(-10r)}{(10)(-7r - 11)}$ Dividing both the numerator and denominator by $10$ gives: $t = \dfrac{-10r}{-7r - 11}$